A cheeky kiss for Valentine's? Only if you're Paul McCartney …

For someone who has just won a Grammy award for an album with a song titled My Valentine, Paul McCartney is surprisingly demure about his romantic credentials.

"Am I a romantic at heart?" he asks. "Yeah, sort of ... I think most people are. 'All you need is love.' There is a reason for saying that ..."

The former Beatle won his 17th Grammy in Los Angeles on Sunday with Kisses on the Bottom, competing in the category of best traditional pop vocal album. Rather than effect the blase demeanour that might be expected of someone who became an MBE at the age of 23, he sounds thrilled.

"With the Beatles we were super blase," he told the Guardian in an interview. "We didn't ever notice anything. We were once up for an Oscar" – two in 1964, in fact, with A Hard Day's Night – "and we didn't even know we were. But now it's lovely, an award. When you see Beyoncé and Adele and Jay-Z – or Jay-Zed, as we call him – up there, it's really nice to be among them."

McCartney won his first Grammy with the Beatles in 1965, when the band were named best new artist, and picked up a lifetime achievement award in 1990. He has received numerous further awards, including a knighthood in 1997 and the grand cross of the order of the sun in Peru. "It's like getting a prize at school," the 70-year-old said. "It's great to get, even if it's not what you aim for ... I don't keep a big cabinet with everything in it."

The Kisses on the Bottom album consists chiefly of covers of old rock'n'roll and jazz numbers, the sort of songs, according to McCartney, that his father would play when he was growing up in Liverpool.

"I've been drawn to that style of music for a long time," he said, noting that he wrote the melody to When I'm Sixty-Four, released on Sgt. Pepper in 1967, almost a decade earlier at the age of 16. "When I became a songwriter, I realised how well constructed those old songs were – there are great melodies, as well as lyrics. People like Cole Porter were quite swotty …"

Kisses on the Bottom also features two McCartney originals, including My Valentine, which he performed with his band at last year's Grammys. "It was written for my wife," he said. "It flowed very easily." McCartney married his third wife, Nancy Shevell, in 2011.

The next album – his 23rd record either as a solo artist or as a member of Wings – is currently in the works. "It's songs I'll be able to play on stage with my band. They're sort of rocking, but there are a couple of ballads as well."

His most recent recording was with Dave Grohl and two other early members of Nirvana on a song called Cut Me Some Slack. It features on the soundtrack to Grohl's documentary Sound City, recently screened at the Sundance film festival, and the band played it live at a hurricane Sandy benefit (video). "It's a bit different from the songs on my album," McCartney said. "It just came about because I'd been given a really hot guitar. It was a rocking jam: really instant and organic."

The 50th anniversary of the Beatles first album, Please Please Me, arrives towards the end of March, and Mc-Cartney contrasted the speed with which the band made such records with the time acts take in the studio now. "Young bands can't believe it when I tell them how quickly we worked," he said. "We'd come in at 10am and be ready to record at 10.30am having tuned up with a cup of tea and a ciggie. Usually no one else would know the song – just me and John – so we'd kick it around, and then we'd have an hour and a half to record it. And then we'd do another one before breaking for lunch for an hour.

"The joke is, those records still sell in the millions, whereas now it seems to take all morning just to get a computer working."

The staunch vegetarian also recently provided the music for a new animated TV advert for his late wife Linda's range of vegetarian food. Of the horsemeat scandal, McCartney said: "It is scandalous – even if it's no big surprise. I don't like to preach, but I think I was right 30 years ago to change my eating habits.

"I don't think the industry will be able to regulate itself. When there's this sort of thing going on, like with the banking scandal, you do hope there'll be some regulations, so people can believe what they're told."

Of his Valentine's Day intentions, McCartney was more coy. "I do have plans but they're un-revealable," he said. "The missus doesn't even know."